1. Field of the Invention
This invention relates to measuring, and more particularly, but not exclusively, it relates to interferometers.
2. Description Relative to the Prior Art
In interferometry it is known that when a straight line fringe pattern is scanned perpendicularly to the fringe orientation, the intensity values detected define a sinusoidal function: EQU I.sub.x =A.sub.x +B.sub.x cos (2.pi.f.sub.o x+.theta..sub.o)
wherein:
x is a spatial variable PA1 A.sub.x is average intensity PA1 B.sub.x is fringe intensity PA1 f.sub.o is spatial frequency PA1 .theta..sub.o is phase value (4.pi..DELTA.L/.lambda.) PA1 .DELTA.is path length difference (L.sub.T -L.sub.R) PA1 .lambda. is wavelength of source. PA1 x.sub.1 =position of the first photodetector. PA1 o&lt;k.sub.x 'x=1, 2, 3, 4
The phase term, .theta..sub.o, is related to the path length difference, .DELTA.L, between the two light beam paths, i.e., the path of fixed length (L.sub.R) and the path of variable length (L.sub.T). Thus, when .DELTA.L changes, so does phase. Therefore, the ability to derive the phase provides direct access to displacement of the probe which controls the path length of the variable length path.
Two known techniques in interferometry have been termed Temporal Phase Shift Interferometry (TPSI) and Four Photodetector (FP), respectively.
TPSI is used in a commercially available instrument for surface profiling work. TPSI relies on a single photodetector to calculate the phase value. Therefore, with the single detector initially detecting an intensity given by EQU I.sub.1 =A+B cos .theta..sub.1
wherein .theta..sub.1 =2.pi.f.sub.o x.sub.1 +.theta..sub.o
after .DELTA.L is changed by .lambda./8, then EQU I.sub.2 =A+B sin .theta..sub.1
and after .DELTA.L is changed by .lambda./8 again, then EQU I.sub.3 =A-B cos .theta..sub.1
The phase term, .theta..sub.1, is given by ##EQU1##
The FP technique uses four photodetectors disposed in a linear array extending perpendicularly to the fringe pattern. The centers of the individual detectors are spaced apart distance d with d being equal to (1/4f.sub.o), i.e., one-fourth the fringe period.
Thus, the intensity detected instantaneously by the four photodetectors is EQU I.sub.1 =A.sub.1 +B.sub.1 cos .theta..sub.1 EQU I.sub.2 =A.sub.2 +B.sub.2 sin .theta..sub.1 EQU I.sub.3 =A.sub.3 -B.sub.3 cos .theta..sub.1 EQU I.sub.4 =A.sub.4 -B.sub.4 sin .theta..sub.1
where
.theta..sub.1 =2.pi.f.sub.o x.sub.1 +.theta..sub.o and
Because four photodetectors are used in FP, as opposed to the single photodetector in TPSI, electrical gain and optical intensity variations render the A.sub.x and B.sub.x coefficients different. This prevents the use of the same simple mathematical manipulation to determine the phase value. The FP technique accepts the variations in coefficients and simply detects transitions above or below the average value terms, A.sub.x. The technique in accordance with the present invention, which might be termed Spatial Phase Shift Interferometry (SPSI), on the other hand, seeks to manipulate the intensity values to a form that allows high resolution phase calculations.